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+//===-- HeuristicSolver.h - Heuristic PBQP Solver --------------*- C++ -*-===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+//
+// Heuristic PBQP solver. This solver is able to perform optimal reductions for
+// nodes of degree 0, 1 or 2. For nodes of degree >2 a plugable heuristic is
+// used to select a node for reduction. 
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_CODEGEN_PBQP_HEURISTICSOLVER_H
+#define LLVM_CODEGEN_PBQP_HEURISTICSOLVER_H
+
+#include "Graph.h"
+#include "Solution.h"
+#include <vector>
+#include <limits>
+
+namespace PBQP {
+
+  /// \brief Heuristic PBQP solver implementation.
+  ///
+  /// This class should usually be created (and destroyed) indirectly via a call
+  /// to HeuristicSolver<HImpl>::solve(Graph&).
+  /// See the comments for HeuristicSolver.
+  ///
+  /// HeuristicSolverImpl provides the R0, R1 and R2 reduction rules,
+  /// backpropagation phase, and maintains the internal copy of the graph on
+  /// which the reduction is carried out (the original being kept to facilitate
+  /// backpropagation).
+  template <typename HImpl>
+  class HeuristicSolverImpl {
+  private:
+
+    typedef typename HImpl::NodeData HeuristicNodeData;
+    typedef typename HImpl::EdgeData HeuristicEdgeData;
+
+    typedef std::list<Graph::EdgeItr> SolverEdges;
+
+  public:
+  
+    /// \brief Iterator type for edges in the solver graph.
+    typedef SolverEdges::iterator SolverEdgeItr;
+
+  private:
+
+    class NodeData {
+    public:
+      NodeData() : solverDegree(0) {}
+
+      HeuristicNodeData& getHeuristicData() { return hData; }
+
+      SolverEdgeItr addSolverEdge(Graph::EdgeItr eItr) {
+        ++solverDegree;
+        return solverEdges.insert(solverEdges.end(), eItr);
+      }
+
+      void removeSolverEdge(SolverEdgeItr seItr) {
+        --solverDegree;
+        solverEdges.erase(seItr);
+      }
+
+      SolverEdgeItr solverEdgesBegin() { return solverEdges.begin(); }
+      SolverEdgeItr solverEdgesEnd() { return solverEdges.end(); }
+      unsigned getSolverDegree() const { return solverDegree; }
+      void clearSolverEdges() {
+        solverDegree = 0;
+        solverEdges.clear(); 
+      }
+      
+    private:
+      HeuristicNodeData hData;
+      unsigned solverDegree;
+      SolverEdges solverEdges;
+    };
+ 
+    class EdgeData {
+    public:
+      HeuristicEdgeData& getHeuristicData() { return hData; }
+
+      void setN1SolverEdgeItr(SolverEdgeItr n1SolverEdgeItr) {
+        this->n1SolverEdgeItr = n1SolverEdgeItr;
+      }
+
+      SolverEdgeItr getN1SolverEdgeItr() { return n1SolverEdgeItr; }
+
+      void setN2SolverEdgeItr(SolverEdgeItr n2SolverEdgeItr){
+        this->n2SolverEdgeItr = n2SolverEdgeItr;
+      }
+
+      SolverEdgeItr getN2SolverEdgeItr() { return n2SolverEdgeItr; }
+
+    private:
+
+      HeuristicEdgeData hData;
+      SolverEdgeItr n1SolverEdgeItr, n2SolverEdgeItr;
+    };
+
+    Graph &g;
+    HImpl h;
+    Solution s;
+    std::vector<Graph::NodeItr> stack;
+
+    typedef std::list<NodeData> NodeDataList;
+    NodeDataList nodeDataList;
+
+    typedef std::list<EdgeData> EdgeDataList;
+    EdgeDataList edgeDataList;
+
+  public:
+
+    /// \brief Construct a heuristic solver implementation to solve the given
+    ///        graph.
+    /// @param g The graph representing the problem instance to be solved.
+    HeuristicSolverImpl(Graph &g) : g(g), h(*this) {}  
+
+    /// \brief Get the graph being solved by this solver.
+    /// @return The graph representing the problem instance being solved by this
+    ///         solver.
+    Graph& getGraph() { return g; }
+
+    /// \brief Get the heuristic data attached to the given node.
+    /// @param nItr Node iterator.
+    /// @return The heuristic data attached to the given node.
+    HeuristicNodeData& getHeuristicNodeData(Graph::NodeItr nItr) {
+      return getSolverNodeData(nItr).getHeuristicData();
+    }
+
+    /// \brief Get the heuristic data attached to the given edge.
+    /// @param eItr Edge iterator.
+    /// @return The heuristic data attached to the given node.
+    HeuristicEdgeData& getHeuristicEdgeData(Graph::EdgeItr eItr) {
+      return getSolverEdgeData(eItr).getHeuristicData();
+    }
+
+    /// \brief Begin iterator for the set of edges adjacent to the given node in
+    ///        the solver graph.
+    /// @param nItr Node iterator.
+    /// @return Begin iterator for the set of edges adjacent to the given node
+    ///         in the solver graph. 
+    SolverEdgeItr solverEdgesBegin(Graph::NodeItr nItr) {
+      return getSolverNodeData(nItr).solverEdgesBegin();
+    }
+
+    /// \brief End iterator for the set of edges adjacent to the given node in
+    ///        the solver graph.
+    /// @param nItr Node iterator.
+    /// @return End iterator for the set of edges adjacent to the given node in
+    ///         the solver graph. 
+    SolverEdgeItr solverEdgesEnd(Graph::NodeItr nItr) {
+      return getSolverNodeData(nItr).solverEdgesEnd();
+    }
+
+    /// \brief Remove a node from the solver graph.
+    /// @param eItr Edge iterator for edge to be removed.
+    ///
+    /// Does <i>not</i> notify the heuristic of the removal. That should be
+    /// done manually if necessary.
+    void removeSolverEdge(Graph::EdgeItr eItr) {
+      EdgeData &eData = getSolverEdgeData(eItr);
+      NodeData &n1Data = getSolverNodeData(g.getEdgeNode1(eItr)),
+               &n2Data = getSolverNodeData(g.getEdgeNode2(eItr));
+
+      n1Data.removeSolverEdge(eData.getN1SolverEdgeItr());
+      n2Data.removeSolverEdge(eData.getN2SolverEdgeItr());
+    }
+
+    /// \brief Compute a solution to the PBQP problem instance with which this
+    ///        heuristic solver was constructed.
+    /// @return A solution to the PBQP problem.
+    ///
+    /// Performs the full PBQP heuristic solver algorithm, including setup,
+    /// calls to the heuristic (which will call back to the reduction rules in
+    /// this class), and cleanup.
+    Solution computeSolution() {
+      setup();
+      h.setup();
+      h.reduce();
+      backpropagate();
+      h.cleanup();
+      cleanup();
+      return s;
+    }
+
+    /// \brief Add to the end of the stack.
+    /// @param nItr Node iterator to add to the reduction stack.
+    void pushToStack(Graph::NodeItr nItr) {
+      getSolverNodeData(nItr).clearSolverEdges();
+      stack.push_back(nItr);
+    }
+
+    /// \brief Returns the solver degree of the given node.
+    /// @param nItr Node iterator for which degree is requested.
+    /// @return Node degree in the <i>solver</i> graph (not the original graph).
+    unsigned getSolverDegree(Graph::NodeItr nItr) {
+      return  getSolverNodeData(nItr).getSolverDegree();
+    }
+
+    /// \brief Set the solution of the given node.
+    /// @param nItr Node iterator to set solution for.
+    /// @param selection Selection for node.
+    void setSolution(const Graph::NodeItr &nItr, unsigned selection) {
+      s.setSelection(nItr, selection);
+
+      for (Graph::AdjEdgeItr aeItr = g.adjEdgesBegin(nItr),
+                             aeEnd = g.adjEdgesEnd(nItr);
+           aeItr != aeEnd; ++aeItr) {
+        Graph::EdgeItr eItr(*aeItr);
+        Graph::NodeItr anItr(g.getEdgeOtherNode(eItr, nItr));
+        getSolverNodeData(anItr).addSolverEdge(eItr);
+      }
+    }
+
+    /// \brief Apply rule R0.
+    /// @param nItr Node iterator for node to apply R0 to.
+    ///
+    /// Node will be automatically pushed to the solver stack.
+    void applyR0(Graph::NodeItr nItr) {
+      assert(getSolverNodeData(nItr).getSolverDegree() == 0 &&
+             "R0 applied to node with degree != 0.");
+
+      // Nothing to do. Just push the node onto the reduction stack.
+      pushToStack(nItr);
+    }
+
+    /// \brief Apply rule R1.
+    /// @param xnItr Node iterator for node to apply R1 to.
+    ///
+    /// Node will be automatically pushed to the solver stack.
+    void applyR1(Graph::NodeItr xnItr) {
+      NodeData &nd = getSolverNodeData(xnItr);
+      assert(nd.getSolverDegree() == 1 &&
+             "R1 applied to node with degree != 1.");
+
+      Graph::EdgeItr eItr = *nd.solverEdgesBegin();
+
+      const Matrix &eCosts = g.getEdgeCosts(eItr);
+      const Vector &xCosts = g.getNodeCosts(xnItr);
+      
+      // Duplicate a little to avoid transposing matrices.
+      if (xnItr == g.getEdgeNode1(eItr)) {
+        Graph::NodeItr ynItr = g.getEdgeNode2(eItr);
+        Vector &yCosts = g.getNodeCosts(ynItr);
+        for (unsigned j = 0; j < yCosts.getLength(); ++j) {
+          PBQPNum min = eCosts[0][j] + xCosts[0];
+          for (unsigned i = 1; i < xCosts.getLength(); ++i) {
+            PBQPNum c = eCosts[i][j] + xCosts[i];
+            if (c < min)
+              min = c;
+          }
+          yCosts[j] += min;
+        }
+        h.handleRemoveEdge(eItr, ynItr);
+     } else {
+        Graph::NodeItr ynItr = g.getEdgeNode1(eItr);
+        Vector &yCosts = g.getNodeCosts(ynItr);
+        for (unsigned i = 0; i < yCosts.getLength(); ++i) {
+          PBQPNum min = eCosts[i][0] + xCosts[0];
+          for (unsigned j = 1; j < xCosts.getLength(); ++j) {
+            PBQPNum c = eCosts[i][j] + xCosts[j];
+            if (c < min)
+              min = c;
+          }
+          yCosts[i] += min;
+        }
+        h.handleRemoveEdge(eItr, ynItr);
+      }
+      removeSolverEdge(eItr);
+      assert(nd.getSolverDegree() == 0 &&
+             "Degree 1 with edge removed should be 0.");
+      pushToStack(xnItr);
+    }
+
+    /// \brief Apply rule R2.
+    /// @param xnItr Node iterator for node to apply R2 to.
+    ///
+    /// Node will be automatically pushed to the solver stack.
+    void applyR2(Graph::NodeItr xnItr) {
+      assert(getSolverNodeData(xnItr).getSolverDegree() == 2 &&
+             "R2 applied to node with degree != 2.");
+
+      NodeData &nd = getSolverNodeData(xnItr);
+      const Vector &xCosts = g.getNodeCosts(xnItr);
+
+      SolverEdgeItr aeItr = nd.solverEdgesBegin();
+      Graph::EdgeItr yxeItr = *aeItr,
+                     zxeItr = *(++aeItr);
+
+      Graph::NodeItr ynItr = g.getEdgeOtherNode(yxeItr, xnItr),
+                     znItr = g.getEdgeOtherNode(zxeItr, xnItr);
+
+      bool flipEdge1 = (g.getEdgeNode1(yxeItr) == xnItr),
+           flipEdge2 = (g.getEdgeNode1(zxeItr) == xnItr);
+
+      const Matrix *yxeCosts = flipEdge1 ?
+        new Matrix(g.getEdgeCosts(yxeItr).transpose()) :
+        &g.getEdgeCosts(yxeItr);
+
+      const Matrix *zxeCosts = flipEdge2 ?
+        new Matrix(g.getEdgeCosts(zxeItr).transpose()) :
+        &g.getEdgeCosts(zxeItr);
+
+      unsigned xLen = xCosts.getLength(),
+               yLen = yxeCosts->getRows(),
+               zLen = zxeCosts->getRows();
+               
+      Matrix delta(yLen, zLen);
+
+      for (unsigned i = 0; i < yLen; ++i) {
+        for (unsigned j = 0; j < zLen; ++j) {
+          PBQPNum min = (*yxeCosts)[i][0] + (*zxeCosts)[j][0] + xCosts[0];
+          for (unsigned k = 1; k < xLen; ++k) {
+            PBQPNum c = (*yxeCosts)[i][k] + (*zxeCosts)[j][k] + xCosts[k];
+            if (c < min) {
+              min = c;
+            }
+          }
+          delta[i][j] = min;
+        }
+      }
+
+      if (flipEdge1)
+        delete yxeCosts;
+
+      if (flipEdge2)
+        delete zxeCosts;
+
+      Graph::EdgeItr yzeItr = g.findEdge(ynItr, znItr);
+      bool addedEdge = false;
+
+      if (yzeItr == g.edgesEnd()) {
+        yzeItr = g.addEdge(ynItr, znItr, delta);
+        addedEdge = true;
+      } else {
+        Matrix &yzeCosts = g.getEdgeCosts(yzeItr);
+        h.preUpdateEdgeCosts(yzeItr);
+        if (ynItr == g.getEdgeNode1(yzeItr)) {
+          yzeCosts += delta;
+        } else {
+          yzeCosts += delta.transpose();
+        }
+      }
+
+      bool nullCostEdge = tryNormaliseEdgeMatrix(yzeItr);
+
+      if (!addedEdge) {
+        // If we modified the edge costs let the heuristic know.
+        h.postUpdateEdgeCosts(yzeItr);
+      }
+ 
+      if (nullCostEdge) {
+        // If this edge ended up null remove it.
+        if (!addedEdge) {
+          // We didn't just add it, so we need to notify the heuristic
+          // and remove it from the solver.
+          h.handleRemoveEdge(yzeItr, ynItr);
+          h.handleRemoveEdge(yzeItr, znItr);
+          removeSolverEdge(yzeItr);
+        }
+        g.removeEdge(yzeItr);
+      } else if (addedEdge) {
+        // If the edge was added, and non-null, finish setting it up, add it to
+        // the solver & notify heuristic.
+        edgeDataList.push_back(EdgeData());
+        g.setEdgeData(yzeItr, &edgeDataList.back());
+        addSolverEdge(yzeItr);
+        h.handleAddEdge(yzeItr);
+      }
+
+      h.handleRemoveEdge(yxeItr, ynItr);
+      removeSolverEdge(yxeItr);
+      h.handleRemoveEdge(zxeItr, znItr);
+      removeSolverEdge(zxeItr);
+
+      pushToStack(xnItr);
+    }
+
+  private:
+
+    NodeData& getSolverNodeData(Graph::NodeItr nItr) {
+      return *static_cast<NodeData*>(g.getNodeData(nItr));
+    }
+
+    EdgeData& getSolverEdgeData(Graph::EdgeItr eItr) {
+      return *static_cast<EdgeData*>(g.getEdgeData(eItr));
+    }
+
+    void addSolverEdge(Graph::EdgeItr eItr) {
+      EdgeData &eData = getSolverEdgeData(eItr);
+      NodeData &n1Data = getSolverNodeData(g.getEdgeNode1(eItr)),
+               &n2Data = getSolverNodeData(g.getEdgeNode2(eItr));
+
+      eData.setN1SolverEdgeItr(n1Data.addSolverEdge(eItr));
+      eData.setN2SolverEdgeItr(n2Data.addSolverEdge(eItr));
+    }
+
+    void setup() {
+      if (h.solverRunSimplify()) {
+        simplify();
+      }
+
+      // Create node data objects.
+      for (Graph::NodeItr nItr = g.nodesBegin(), nEnd = g.nodesEnd();
+	       nItr != nEnd; ++nItr) {
+        nodeDataList.push_back(NodeData());
+        g.setNodeData(nItr, &nodeDataList.back());
+      }
+
+      // Create edge data objects.
+      for (Graph::EdgeItr eItr = g.edgesBegin(), eEnd = g.edgesEnd();
+           eItr != eEnd; ++eItr) {
+        edgeDataList.push_back(EdgeData());
+        g.setEdgeData(eItr, &edgeDataList.back());
+        addSolverEdge(eItr);
+      }
+    }
+
+    void simplify() {
+      disconnectTrivialNodes();
+      eliminateIndependentEdges();
+    }
+
+    // Eliminate trivial nodes.
+    void disconnectTrivialNodes() {
+      unsigned numDisconnected = 0;
+
+      for (Graph::NodeItr nItr = g.nodesBegin(), nEnd = g.nodesEnd();
+           nItr != nEnd; ++nItr) {
+
+        if (g.getNodeCosts(nItr).getLength() == 1) {
+
+          std::vector<Graph::EdgeItr> edgesToRemove;
+
+          for (Graph::AdjEdgeItr aeItr = g.adjEdgesBegin(nItr),
+                                 aeEnd = g.adjEdgesEnd(nItr);
+               aeItr != aeEnd; ++aeItr) {
+
+            Graph::EdgeItr eItr = *aeItr;
+
+            if (g.getEdgeNode1(eItr) == nItr) {
+              Graph::NodeItr otherNodeItr = g.getEdgeNode2(eItr);
+              g.getNodeCosts(otherNodeItr) +=
+                g.getEdgeCosts(eItr).getRowAsVector(0);
+            }
+            else {
+              Graph::NodeItr otherNodeItr = g.getEdgeNode1(eItr);
+              g.getNodeCosts(otherNodeItr) +=
+                g.getEdgeCosts(eItr).getColAsVector(0);
+            }
+
+            edgesToRemove.push_back(eItr);
+          }
+
+          if (!edgesToRemove.empty())
+            ++numDisconnected;
+
+          while (!edgesToRemove.empty()) {
+            g.removeEdge(edgesToRemove.back());
+            edgesToRemove.pop_back();
+          }
+        }
+      }
+    }
+
+    void eliminateIndependentEdges() {
+      std::vector<Graph::EdgeItr> edgesToProcess;
+      unsigned numEliminated = 0;
+
+      for (Graph::EdgeItr eItr = g.edgesBegin(), eEnd = g.edgesEnd();
+           eItr != eEnd; ++eItr) {
+        edgesToProcess.push_back(eItr);
+      }
+
+      while (!edgesToProcess.empty()) {
+        if (tryToEliminateEdge(edgesToProcess.back()))
+          ++numEliminated;
+        edgesToProcess.pop_back();
+      }
+    }
+
+    bool tryToEliminateEdge(Graph::EdgeItr eItr) {
+      if (tryNormaliseEdgeMatrix(eItr)) {
+        g.removeEdge(eItr);
+        return true; 
+      }
+      return false;
+    }
+
+    bool tryNormaliseEdgeMatrix(Graph::EdgeItr &eItr) {
+
+      const PBQPNum infinity = std::numeric_limits<PBQPNum>::infinity();
+
+      Matrix &edgeCosts = g.getEdgeCosts(eItr);
+      Vector &uCosts = g.getNodeCosts(g.getEdgeNode1(eItr)),
+             &vCosts = g.getNodeCosts(g.getEdgeNode2(eItr));
+
+      for (unsigned r = 0; r < edgeCosts.getRows(); ++r) {
+        PBQPNum rowMin = infinity;
+
+        for (unsigned c = 0; c < edgeCosts.getCols(); ++c) {
+          if (vCosts[c] != infinity && edgeCosts[r][c] < rowMin)
+            rowMin = edgeCosts[r][c];
+        }
+
+        uCosts[r] += rowMin;
+
+        if (rowMin != infinity) {
+          edgeCosts.subFromRow(r, rowMin);
+        }
+        else {
+          edgeCosts.setRow(r, 0);
+        }
+      }
+
+      for (unsigned c = 0; c < edgeCosts.getCols(); ++c) {
+        PBQPNum colMin = infinity;
+
+        for (unsigned r = 0; r < edgeCosts.getRows(); ++r) {
+          if (uCosts[r] != infinity && edgeCosts[r][c] < colMin)
+            colMin = edgeCosts[r][c];
+        }
+
+        vCosts[c] += colMin;
+
+        if (colMin != infinity) {
+          edgeCosts.subFromCol(c, colMin);
+        }
+        else {
+          edgeCosts.setCol(c, 0);
+        }
+      }
+
+      return edgeCosts.isZero();
+    }
+
+    void backpropagate() {
+      while (!stack.empty()) {
+        computeSolution(stack.back());
+        stack.pop_back();
+      }
+    }
+
+    void computeSolution(Graph::NodeItr nItr) {
+
+      NodeData &nodeData = getSolverNodeData(nItr);
+
+      Vector v(g.getNodeCosts(nItr));
+
+      // Solve based on existing solved edges.
+      for (SolverEdgeItr solvedEdgeItr = nodeData.solverEdgesBegin(),
+                         solvedEdgeEnd = nodeData.solverEdgesEnd();
+           solvedEdgeItr != solvedEdgeEnd; ++solvedEdgeItr) {
+
+        Graph::EdgeItr eItr(*solvedEdgeItr);
+        Matrix &edgeCosts = g.getEdgeCosts(eItr);
+
+        if (nItr == g.getEdgeNode1(eItr)) {
+          Graph::NodeItr adjNode(g.getEdgeNode2(eItr));
+          unsigned adjSolution = s.getSelection(adjNode);
+          v += edgeCosts.getColAsVector(adjSolution);
+        }
+        else {
+          Graph::NodeItr adjNode(g.getEdgeNode1(eItr));
+          unsigned adjSolution = s.getSelection(adjNode);
+          v += edgeCosts.getRowAsVector(adjSolution);
+        }
+
+      }
+
+      setSolution(nItr, v.minIndex());
+    }
+
+    void cleanup() {
+      h.cleanup();
+      nodeDataList.clear();
+      edgeDataList.clear();
+    }
+  };
+
+  /// \brief PBQP heuristic solver class.
+  ///
+  /// Given a PBQP Graph g representing a PBQP problem, you can find a solution
+  /// by calling
+  /// <tt>Solution s = HeuristicSolver<H>::solve(g);</tt>
+  ///
+  /// The choice of heuristic for the H parameter will affect both the solver
+  /// speed and solution quality. The heuristic should be chosen based on the
+  /// nature of the problem being solved.
+  /// Currently the only solver included with LLVM is the Briggs heuristic for
+  /// register allocation.
+  template <typename HImpl>
+  class HeuristicSolver {
+  public:
+    static Solution solve(Graph &g) {
+      HeuristicSolverImpl<HImpl> hs(g);
+      return hs.computeSolution();
+    }
+  };
+
+}
+
+#endif // LLVM_CODEGEN_PBQP_HEURISTICSOLVER_H